All posts tagged ‘achilles’

Sean S.'s awesome contribution to projectile motion: "Wow, projectile motion, I haven't done this since high school; this is great!"

This week’s puzzle asked how to shoot an arrow as far as possible from the walls of Troy. Ah yeah, projectile motion, baby! (Or as Laurion wrote, “Oooh, trajectory calculations!” Thank you, Laurion….me too!) And if you ever took physics 101, you know that in the absence of a constant, you can disregard wind resistance (not really — but so go physics 101 problems). Here was this week’s question:

You, Paris, have the luxury of launching an arrow at faraway Achilles either from the ramparts above the Hesperian Gate at a height of exactly 8 meters. Or you can stand atop Priam’s palace. This gains you another 7 meters of launch height, but it costs you 15 meters of horizontal distance. If the arrow leaves your bow at a somewhat modest 70 meters per second, are you best taking your pot-shot at far-off Achilles from the ramparts or the palace? Which perch offers the farthest reach?

Should you, Paris, shoot from the ramparts or the tippy-top of Priam's palace to best reach far-off Achilles?

That darn Achilles has been joyriding around the walls of Troy again, and with Hector stuck to his bumper, no less! The city’s best archers have hit Achilles with a thousand errors, but cocky Achilles doesn’t seem to get wet in rainstorms and certainly isn’t bothered by Troy’s rain of arrows. But you have a feeling you might be different. Yes, Paris, something tells you if you could shoot an arrow far enough, it would have a simply divine chance of finding its mark.

You have the luxury of launching either from the ramparts above the Hesperian Gate at a height of exactly 8 meters. Or you can stand atop Priam’s palace. This gains you another 7 meters of launch height, but it costs you 15 meters of horizontal distance. If the arrow leaves your bow at a somewhat modest 70 meters per second, are you best taking your pot-shot at far-off Achilles from the ramparts or the palace? Which perch offers the farthest reach?